The disaster happened in waters between Italy and Libya, based on accounts from 41 survivors who were rescued on April 16 by a merchant ship, the UNHCR said.
The agency said that if confirmed, it would be one of the deadliest tragedies in the Mediterranean in the last year.
The survivors said they had been among 100 to 200 people who left a town near Tobruk, Libya, on a smugglers’ boat last week.
The agency said that “after sailing for several hours, the smugglers in charge of the boat attempted to transfer the passengers to a larger ship carrying hundreds of people in terribly overcrowded conditions”.
“At one point during the transfer, the larger boat capsized and sank,” the UNHCR said in a statement, saying that its staff had visited the survivors at a local stadium in Kalamata, Greece, where they have been housed by authorities while they undergo “police procedures”.
Barbara Molinario, a Rome-based spokeswoman for the UNHCR, said details remained unclear and said its staffers did not want to press the survivors too hard.
The statements offered the most official comment yet following repeated news reports about the incident in recent days.
Somalia’s president, prime minister and parliamentary speaker on Monday issued a joint statement over an unconfirmed report about the incident.
Reports of the drownings circulated among families and on social media, but they had not been confirmed by coast guard authorities in Italy, Greece, Libya or Egypt.
More than one million migrants and refugees crossed the Mediterranean last year - mostly refugees from war in Afghanistan, Iraq and Syria fleeing to Greece, and the European Union, via Turkey. However, the longer Libya-Italy route has traditionally seen more deaths.
Facing internal divisions, the EU has struggled to cope with the influx, and the UNHCR reiterated its longstanding call for more “regular pathways” to Europe, such as with resettlement and humanitarian admission programmes, family reunification, private sponsorship and student and work visas.
Rights groups have repeatedly criticised a new Turkey-EU deal to curtail the flood of refugees into Europe, raising questions about the safety of Syrian refugees on both sides of the Turkish border.
Human Rights Watch urged Turkey to allow Syrians displaced by government shelling to cross the border to safety. The advocacy groups said the Syrian army hit two migrant camps on April 13 and 15, triggering an exodus of 3,000 people.
Last week, the rights group said Turkish border guards had shot at Syrians escaping an Islamic State offensive.
Turkey, home to 2.7 million Syrian refugees, rejects the claim and says it has an open-door policy towards migrants, but new arrivals are rare.
The rights group says tens of thousands of civilians are trapped along Turkey’s border.